Investigation of Free Particle Propagator with Generalized Uncertainty Problem

TL;DR

This paper derives the free particle propagator within a generalized uncertainty principle framework, extending quantum mechanics to include minimal length effects and recovering standard results when the minimal length parameter is zero.

Contribution

It introduces a method to obtain the free particle propagator under a generalized uncertainty principle, highlighting the impact of minimal length on quantum evolution.

Findings

Derived the free particle propagator with GUP modifications

Showed the standard quantum mechanics propagator is recovered when minimal length is zero

Provided a differential equation approach to incorporate GUP effects

Abstract

We consider the Schrodinger equation with a generalized uncertainty principle for a free particle. We then transform the problem into a second ordinary differential equation and thereby obtain the corresponding propagator. The result of ordinary quantum mechanics is recovered for vanishing minimal length parameter.